Open Access
April 2018 Detecting rare and faint signals via thresholding maximum likelihood estimators
Yumou Qiu, Song Xi Chen, Dan Nettleton
Ann. Statist. 46(2): 895-923 (April 2018). DOI: 10.1214/17-AOS1574


Motivated by the analysis of RNA sequencing (RNA-seq) data for genes differentially expressed across multiple conditions, we consider detecting rare and faint signals in high-dimensional response variables. We address the signal detection problem under a general framework, which includes generalized linear models for count-valued responses as special cases. We propose a test statistic that carries out a multi-level thresholding on maximum likelihood estimators (MLEs) of the signals, based on a new Cramér-type moderate deviation result for multidimensional MLEs. Based on the multi-level thresholding test, a multiple testing procedure is proposed for signal identification. Numerical simulations and a case study on maize RNA-seq data are conducted to demonstrate the effectiveness of the proposed approaches on signal detection and identification.


Download Citation

Yumou Qiu. Song Xi Chen. Dan Nettleton. "Detecting rare and faint signals via thresholding maximum likelihood estimators." Ann. Statist. 46 (2) 895 - 923, April 2018.


Received: 1 August 2016; Revised: 1 April 2017; Published: April 2018
First available in Project Euclid: 3 April 2018

zbMATH: 06870283
MathSciNet: MR3782388
Digital Object Identifier: 10.1214/17-AOS1574

Primary: 62H15
Secondary: 62G20 , 62G32

Keywords: Detection boundary , false discovery proportion , generalized linear model , Moderate deviation , multiple testing procedure , RNA-seq data

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 2 • April 2018
Back to Top